Contents -- Preface -- 1 A Note on Finitely Generated Semigroups of Regular Languages S. Afonin and E. Khazova -- 1. Introduction -- 2. Preliminaries -- 3. Membership and word problems -- 4. Connection with automatic semigroups -- References -- 2 Complete Reducibility of Pseudovarieties J. Almeida, J. C. Costa and M. Zeitoun -- 1. Introduction -- 2. How we are led to systems of equations -- 3. Simplifications -- 4. Further simplifications for the case of R -- 5. Complete reducibility of R -- 6. General strategy of the proof -- Appendix -- Acknowledgments -- References -- 3 Finite Generation of P-semigroups with Almost G-invariant Idempotents C. A. Carvalho -- 1. Introduction -- 2. Proof of the Main Theorem -- 3. Example -- Acknowledgments -- References -- 4 Open Problems on Regular Languages: A Historical Perspective L. Chaubard and J.- E. Pin -- 1. Operations on languages -- 2. Rational and recognisable languages -- 3. Star-height -- 3.1. Star-free languages -- 3.2. The star-height problem -- 4. Concatenation hierarchies -- 5. Back to the star-height problem -- 6. Shuffle product -- 7. Conclusion -- References -- 5 Solving Systems of Equations Modulo Pseudovarieties of Abelian Groups and Hyperdecidability M. Delgado, A. Masuda and B. Steinberg -- 1. Introduction -- 2. Solving systems modulo pseudovarieties of abelian groups -- 2.1. Proof of Theorem 1.1 -- 2.2. Proof of Theorem 1.2 -- Bibliography -- 6 Finite Residue Class Rings of Integers Modulo n from the Viewpoint of Global Semigroup Theory A. Egri-Nagy and C. L. Nehaniv -- 1. Introduction -- 2. Mathematical Preliminaries and Notations -- 3. Holonomy Decomposition Theorem -- 4. Decomposition of the Rings of Integers Modulo n -- 4.1. Representation -- 4.2. The Extended Set of Images -- 4.3. Subduction, Equivalence Relation, and the Tiling Picture -- 4.4. Number of Levels.

4.5. Number of States -- 4.6. Holonomy Group Components -- 5. Examples of Decomposition -- 6. Conclusion and Future Work -- References -- 7 A P-theorem for Ordered Groupoids N. D. Gilbert -- 1. Introduction -- 2. Levelling ordered groupoids -- 2.1. Incompressible ordered groupoids -- 2.1.1. E-unitary inverse semigroups -- 2.2. -transitive ordered groupoids -- 3. Groupoids acting on posets -- 4. The P-theorem -- 4.1. The Gomes-Howie P-theorem -- 5. Actions on cosets -- 5.1. A Clifford semigroup -- 5.2. Free products with amalgamation -- 5.3. HNN extensions -- References -- 8 On the Finite Basis Problem for the Monoids of Extensive Transformations I. A. Goldberg -- 1. Introduction -- 2. Proof of Theorem 1.1 -- References -- 9 A Freiheitssatz for Subsemigroups of One-relator Groups with Small Cancellation Condition A. Juh asz -- Introduction -- 1. Proof of the Theorem -- 2. Preliminary results on words and diagrams -- 2.1. Words -- 2.2. Diagrams -- 3. Piece configurations of 1-corner regions and 2-corner regions -- 4. Proposition 4.1 and its proof -- References -- 10 Wreath Product Decompositions for Triangular Matrix Semigroups M. Kambites and B. Steinberg -- 1. Introduction -- 2. Wreath Products, Division and Complexity -- 3. Triangular Matrix Semigroups -- 4. Decompositions for Triangular Matrix Semigroups -- 5. Comparison with Depth Decomposition -- Acknowledgments -- References -- 11 In McAlister's Footsteps: A Random Ramble around the P-theorem M. V. Lawson and S. W. Margolis -- 1. A primer on categories and inverse semigroups -- 2. The P-theorem -- 3. Partial group actions -- 4. Ordered groupoids -- 5. Extensions of semilattices by groups, the derived category and global semigroup theory -- 6. Cancellative categories -- References -- 12 On the Structure of the Lattice of Combinatorial Rees{Sushkevich Varieties E. W. H. Lee and M. V. Volkov.

Introduction -- 1. The variety A2 and a decomposition of its subvariety lattice into intervals -- 2. Regular elements in semigroups from A2 and their representation by words -- 3. Kublanovskii's lemma and the scheme of its usage -- 4. Main results -- Acknowledgments -- References -- 13 On Trivializers and Subsemigroups A. Malheiro -- 1. Introduction -- 2. Preliminaries -- 2.1. Presentations and rewriting systems -- 2.2. About 2-complexes -- 2.3. The Squier complex -- 3. A general presentation for a subsemigroup -- 4. A general trivializer for a subsemigroup -- 5. An application to bands of monoids -- Acknowledgments -- References -- 14 Semilattice Ordered Inverse Semigroups D. B. McAlister -- 1. Introduction -- 2. The free monogenic semilatticed inverse semigroup -- 3. Totally ordered !-regular semigroups. -- 4. E-unitary inverse semigroups. -- 5. Semidirect product embeddings -- References -- 15 Isomorphism Problems for Transformation Semigroups S. Mendes-Gon calves -- 1. Introduction -- 2. Isomorphisms between transformation semigroups -- 3. Isomorphisms between linear transformation semigroups -- 4. Isomorphisms between Baer-Levi semigroups -- Acknowledgments -- References -- 16 On McAlister's Monoid and Its Contracted Algebra W. D. Munn -- 1. The McAlister monoid Mx -- 2. The contracted monoid algebra of MX -- Acknowledgments -- References -- 17 Relative Monoid Presentations and Finite Derivation Type F. Otto -- 1. Introduction -- 2. Relative monoid presentations -- 3. The Squier complex of a relative monoid presentation -- 4. F-G-sequences -- 5. Application -- References -- 18 Literal Varieties and Pseudovarieties of Homomorphisms onto Abelian Groups L. Pol ak -- 1. Introduction -- 2. Preliminaries -- 3. Varieties of homomorphisms onto abelian groups -- 4. Pseudovarieties of finite homomorphisms onto abelian groups -- 5. Corresponding languages.

6. Final Remarks -- References -- 19 Factorizability in Certain Classes over Inverse Semigroups M. B. Szendrei . -- 1. Preliminaries -- 2. Inverse semigroups -- 2.1. First approach -- 2.2. Second approach -- 3. More general classes of semigroups -- 3.1. First approach -- 3.2. Second approach -- Acknowledgments -- References.